Surprising Geometric Solutions: A Projective Geometry Approach

This book introduces the major ideas of projective geometry through clear explanations, visual intuition, and hands-on problem solving. Projective geometry opens a window into the deeper patterns of space, perspective, and form. While Euclidean geometry guides familiar constructions—drawing points, lines, and circles with a straightedge and compass—projective geometry goes further, encompassing hyperbolic and elliptic geometries and revealing the rules behind the way we see the world. Why do railway tracks appear to converge in the distance? Why does a tilted coin look like an ellipse? These are not illusions—they are manifestations of projective geometry at work.Readers will explore classical constructions and fundamental geometrical ideas through a fresh lens, building towards an exploration of key projective principles such as duality and invariance. Highlighting real-world applications in mathematics, physics, computer science, art and architecture, the book presents projective geometry not just as a mathematical discipline, but as a way of seeing. Whether you are a student, teacher, or curious mind, this book offers a new perspective on geometry—not just what we measure, but how we perceive and understand the world around us.